Finite Group DatabasebetaFinite Group Databasebeta| order | 26166 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C49⋊C3×D89 |
| unambiguous semidirect product | C89⋊(C2×C49⋊C3) |
| unambiguous semidirect product | (C49×D89)⋊C3 |
| Fitting, derived, Hall | C49×C89 ⋊ C2×C3 |
| Hall | C89×C49⋊C3 ⋊ C2 |
| Hall | C49×D89 ⋊ C3 |
| Sylow | C89 ⋊ C2×C49⋊C3 |
| Sylow | C49 ⋊ C3×D89 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C49×C89 | C2×C3 |
| Frattini | C7 | ΓL(1,𝔽8)×D89 |
| socle | C7×C89 | C2×ΓL(1,𝔽8) |
| LCS | G ▷ C49×C89 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4361 |
874 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26166, 10);